D3 branes in a Melvin universe: A new realm for gravitational holography

The decoupling limit of a certain configuration of D3 branes in a Melvin universe defines a sector of string theory known as puff field theory (PFT)--a theory with nonlocal dynamics but without gravity. In this work, we present a systematic analysis of the nonlocal states of strongly coupled PFT using gravitational holography. And we are led to a remarkable new holographic dictionary. We show that the theory admits states that may be viewed as brane protrusions from the D3 brane worldvolume. The footprint of a protrusion has finite size--the scale of nonlocality in the PFT--and corresponds to an operator insertion in the PFT. We compute correlators of these states, and we demonstrate that only part of the holographic bulk is explored by this computation. We then show that the remaining space holographically encodes the dynamics of the D3 brane tentacles. The two sectors are coupled: in this holographic description, this is realized via quantum entanglement across a holographic screen - a throat in the geometry - that splits the bulk into the two regions in question. We then propose a description of PFT through a direct product of two Fock spaces--akin to other nonlocal settings that employ quantum group structures.